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There is a DC battery or AC power supply, then there is a resistance R and a capacitor  which are all connected in series.
  There ma y be a switch to close the circuit at t = 0.

the time constant for charging or  discharging the capacitor = RC.
After the capacitor gets charged quickly to the voltage of the dc supply, there is no more current in the circuit.

for AC circuit, the capacitor continuously charges and discharges.  there is heat dissipation in the resistance.

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